EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in the deep neural networks. In this paper, we propose a QR-based ED method dedicated to the application scenarios of computer vision. Our proposed method performs the ED entirely by batched matrix/vector multiplication, which processes all the matrices simultaneously and thus fully utilizes the power of GPUs. Our technique is based on the explicit QR iterations by Givens rotation with double Wilkinson shifts. With several acceleration techniques, the time complexity of QR iterations is reduced from $O{(}n^5{)}$ to $O{(}n^3{)}$. The numerical test shows that for small and medium batched matrices (\emph{e.g.,} $dim{<}32$) our method can be much faster than the Pytorch SVD function. Experimental results on visual recognition and image generation demonstrate that our methods also achieve competitive performances.

本文提出了一种基于QR分解的、专门针对计算机视觉应用情景下的批量矩阵/向量乘法计算的EigenDecomposition方法，通过使用显式QR迭代和多个加速技巧，将QR迭代的时间复杂度从O(n^5)降低到O(n^3)，在小规模和中规模批量矩阵的场景下可以显著提升计算速度，并且在图像识别和生成方面有着较好的表现。

小型和中型矩阵的批量高效特征分解